Quantitative Finance for Physicists

Both CAPM and APT consider only one time period and treat the

risk-free interest rate as an exogenous parameter. However, in real

life, investors make investing and consumption decisions that are in

effect for long periods of time. An interesting direction in the port-

folio theory (that is beyond the scope of this book) describes invest-

ment and consumption processes within a single framework. The risk-

free interest rate is then determined by the consumption growth and

by investor risk aversion. The most prominent theories in this direc-

tion are the intertemporal CAPM (ICAPM) and the consumption

CAPM (CCAPM) [2, 3, 7].

10.4 ARBITRAGE TRADING STRATEGIES

The simple investment strategy means ‘‘buy and hold’’ securities

of ‘‘good’’ companies until their performance worsens, then sell them

and buy better assets. A more sophisticated approach is sensitive to

changing economic environment and an investor’s risk tolerance,

which implies periodic rebalancing of the investor portfolio between

cash, fixed income, and equities. Proponents of the conservative

investment strategy believe that this is everything an investor should

do while investing for the ‘‘long run.’’ Yet, many investors are not

satisfied with the long-term expectations: they want to make money

at all times (and who could blame them?). Several concepts being

intensively explored by a number of financial institutions, particu-

larly by the hedge funds, are called market-neutral strategies.

In a nutshell, market-neutral strategy implies hedging the risk of

financial losses by combining long and short positions in the port-

folio. For example, consider two companies within the same industry,

A and B, one of which (A) yields consistently higher returns. The

strategy named pair trading involves simultaneously buying shares

A and short selling shares B. Obviously, if the entire sector rises,

this strategy does not bring as much money as simply buying

shares A. However, if the entire market falls, presumably shares B

will have higher losses than shares A. Then the profits from short

selling shares B would more than compensate for the losses from

buying shares A.

118 Portfolio Management

Specifics of the hedging strategies are not widely advertised for

obvious reasons: the more investors target the same market ineffi-

ciency, the faster it is wiped out. Several directions in the market-

neutral investing are described in the literature [8].

Convertible arbitrage. Convertible bonds are bonds that can be

converted into shares of the same company. Convertible bonds

often decline less in a falling market than shares of the same company

do. Hence, the idea of the convertible arbitrage is buying convertible

bonds and short selling the underlying stocks.

Fixed-income arbitrage. This strategy implies taking long and short

positions in different fixed-income securities. By watching the correl-

ations between different securities, one can buy those securities

that seem to become underpriced and sell short those that look

overpriced.

Mortgage-backed securities (MBS) arbitrage. MBS is actually a

form of fixed income with a prepayment option. Yet, there are so

many different MBS that this makes them a separate business.

Merger arbitrage. This form of arbitrage involves buying shares of a

company that is being bought and short selling the shares of the buying

company. The rationale behind this strategy is that companies are

usually acquired at a premium, which sends down the stock prices of

acquiring companies.

Equity hedge. This strategy is not exactly the market-neutral one, as

the ratio between long and short equity positions may vary depending

on the market conditions. Sometimes one of the positions is the stock

index future while the other positions are the stocks that constitute

this index (so-called index arbitrage). Pair trading also fits this

strategy.

Equity market-neutral strategy and statistical arbitrage. Nicholas

discerns these two strategies by the level of constraints (availability of

resources) imposed upon the portfolio manager [8]. The common

feature of these strategies is that (in contrast to the equity hedge),

they require complete offsetting of the long positions by the short

positions. Statistical arbitrage implies fewer constraints in the devel-

opment of quantitative models and hence a lower amount of the

portfolio manager’s discretion in constructing a portfolio.

Relative value arbitrage. This is a synthetic approach that may

embrace several hedging strategies and different securities including

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